If the selling price of an article is doubled, then its loss per cent is converted into equal profit per cent. The loss per cent on the article is

Options

A. `26"" (2)/(3) %`
B. `33 %`
C. `33"" (1)/(3) %`
D. 0.34

Answer

To solve the problem step by step, we need to establish the relationship between the cost price (CP), selling price (SP), loss percentage, and profit percentage.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that if the selling price of an article is doubled, the loss percentage becomes equal to the profit percentage. We need to find the loss percentage.

2. **Let’s Define Variables**:
- Let the cost price (CP) of the article be \( CP = x \).
- Let the original selling price (SP) be \( SP = y \).

3. **Loss Calculation**:
Since the selling price is less than the cost price (indicating a loss), the loss percentage can be calculated as:
\[ \text{Loss Percentage} = \frac{CP - SP}{CP} \times 100 = \frac{x - y}{x} \times 100 \]

4. **Doubling the Selling Price**:
When the selling price is doubled, the new selling price becomes:
\[ \text{New SP} = 2y \]

5. **Profit Calculation**:
When the selling price is doubled, the profit percentage can be calculated as:
\[ \text{Profit Percentage} = \frac{SP - CP}{CP} \times 100 = \frac{2y - x}{x} \times 100 \]

6. **Setting Loss Percentage Equal to Profit Percentage**:
According to the problem, the loss percentage equals the profit percentage when the selling price is doubled:
\[ \frac{x - y}{x} \times 100 = \frac{2y - x}{x} \times 100 \]

7. **Eliminating the Common Factor**:
We can eliminate the \( \times 100 \) and \( x \) from both sides:
\[ x - y = 2y - x \]

8. **Rearranging the Equation**:
Rearranging gives:
\[ x + x = 2y + y \]
\[ 2x = 3y \]
\[ y = \frac{2}{3}x \]

9. **Finding the Loss Percentage**:
Now substituting \( y \) back into the loss percentage formula:
\[ \text{Loss Percentage} = \frac{x - y}{x} \times 100 = \frac{x - \frac{2}{3}x}{x} \times 100 \]
\[ = \frac{\frac{1}{3}x}{x} \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

10. **Final Answer**:
Therefore, the loss percentage is:
\[ \text{Loss Percentage} = 33 \frac{1}{3} \% \]